Rules of Probability

When you want the probability of two or more things happening you multiply their probabilities together.

For example:

For two events A and B,

p (A and B) = p (A) x p (B)

For example, the probability of rolling a 6 on a dice and getting Heads on the toss of a coin is:

An important condition

The events must be independent.

This means that one of them happening must not change the probability of the other one happening.

For example:

If you pick a card from a pack of 52, p(King)=

If you pick two cards one after the other and want to know the probability of two kings but don't put the first card back, then you cannot use the 'and' rule because there are only 51 cards the second time (the probability has changed).

Another example: Say you wanted to find the probability of it raining and finding someone carrying an umbrella. These two events are said to be dependant i.e. if it is raining it is more likely that you will find someone carrying an umbrella.

So the probability of finding an umbrella carrier changes. You could not use the 'and' rule in this example as the two events are not independant.

If you want one outcome or another outcome then you add their probabilities together.

For example:

For two events A and B,

p (A or B) = p (A) + p (B)

For example:

The probability of getting a 6 or a 5 on the roll of a dice is:

An important condition

The events must be mutually exclusive.

This means that they must not be able to happen at the same time as each other.

For example, the probability of drawing a King or a Club from a pack of 52 cards cannot be done by adding their probabilities because a King can also be a Club so you would have counted one of the Kings twice - they are not mutually exclusive.

Below is a quick test to check that you understand all the rules. Drag and drop the four panels into the correct gaps and then mark your answer to see how you got on: